Roy Disney's Shamrock Activist Value Fund has just bought $2 million in shares of the change-counter company and now holds more than a 5% stake.

ROY DISNEY'S SHAMROCK ACTIVIST VALUE FUND is hoping that the nickels and dimes consumers dump into Coinstar machines will mint some hard cash for the activist shareholder.

Coinstar operates the self-service machines found at grocery stores that let consumers exchange coins for dollar bills or gift cards for retailers such as Starbucks, Amazon.com and Apple's iTunes. The slightly larger entertainment...